Set theory: Urelements and classes, where to planets and moons fit?

Question

As I understand it, urelements can be members of sets but sets can't be members of urelements. I'm not sure how to describe this situation. How does ZF fit in a scenario I'm trying to explain (open to rewording by someone that knows) by saying the universe is composed of urelements being proper classes (collection too large to be an object or set) containing planets, moons, asteroids, blackholes. Then let's take an object from one of those proper classes, let's say planet Earth, and then I put into place a discretization process where Earth is divided into a set of geometric elements? What is a urelement, proper class, etc. in this scenario?

Answer 1

In ZF(C) there are no urelements.

An urelement is an object that is not a set (In the context of ZF(C)-like theories like ZFA [ZF where extensionality changed a bit and we do have urelements], $x$ is an urelement if it is not the empty set, and $a\in x$ is always false).

Proper classes are (in ZF(C)) not an object, a proper class is simply a formula $φ(x)$ that we abbreviate $φ(a)$ to be $a∈φ$.

What urelement supposed to represent is an "atomic objects", they supposed to be thought of as the stuff that build the universe up and they cannot be broken down to smaller stuff.

A proper class is something we use to describe collections that are "too big" (in some sense) to be a set, for example the collection of all sets is a proper class, it is "too big" to be a set (it is as big as it gets)

Proper classes don't make sense to be asked about outside of the context of a set theory, as the "proper" means to distinguish them from sets, in any other example all collections are simply "classes", and "urelements" are the building blocks

Answer 2

The word "universe" in math does not refer to the physical universe, and physical objects are not mathematical objects. There are many ways to model physical objects using set theory, but how you do it depends on which logical properties you're trying to capture. A planet could be described by a urelement, a set, or a proper class.